Six unit squares can be joined
along their edges to form 35 different
hexominos, the simplest being a one
by six rectangle.
How many of these
hexominos can be folded along edges
joining the squares to form a unit
cube?
A rotation or reflection is not
considered to be a different hexomino.
***Adapted from a problem appearing in The BENT, Brain Ticklers,Spring Collection 2008.
If any hexomino has four squares meeting at a corner, that would be unfoldable. In the layouts below, these hexominos are represented
by six asterisks.
For the others, one square was chosen as the front (F) and the resulting positions of the remainder are determined by the folding. In most cases at least one face of the cube remains uncovered while one or more faces receive more than one square cover.
There are 11 where each face of the cube is covered/formed exactly once.
F=Front, Bt=Bottom, Bk=Back, T=Top, L=Left, R=Right
F
Bt F R F F T * *
Bk Bt Bt R Bt F R * * F R
T Bk Bk Bk R Bt * Bt
F T T T Bk * Bk R
Bt F F F T T
F R * F R Bk F L F R F R F R
Bt * * Bt Bt R T Bt L Bt Bt
Bk * * Bk Bk Bk Bk L Bk
T R * T T T T T
CUBE CUBE CUBE
L *
F R F F T T T * *
Bt Bt R L Bt R F R Bk F R F R * *
Bk L Bk Bk Bt Bt Bt *
L T T T Bk Bk R Bk
CUBE CUBE CUBE CUBE
T T T T Bk
* * L F R * * * F R F R Bk F R F R Bk
* * Bt * * L Bt Bt Bt Bt Bt
* * Bk * Bk Bk Bk Bk
CUBE CUBE
F F T T F R * * * T
Bt R T L F R Bt * * * * * * * * F R
Bk Bt L Bk * * * * * * * L Bt
T Bk
CUBE CUBE
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Posted by Charlie
on 2024-06-13 07:22:25 |
solution
